If the volume of the box is 112 in3, find the value of x (in inches). (Assume that all the dimensions in the figure are in inches.)

X=4

Step-by-step explanation:

4x(x+3)=112

4x^2+12x=112

x^2+3x=28

x^2+3x-28=0

(X+7)(x-4)=0

X=-7 or x=4

volume of cuboid =l×b×h

112in³=(x+3)×x×4

112in³/4=x²+3x

28=x²+3x

x²+3x-28=0

x²+7x-4x-28=0

x(x+7)-4(x+7)=0

(x+7)(x-4)=0

either

x=-7(rejected length or breadth or height will be always positive)

or

x=4in

value of x =4in

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for